Contribution of mathematical modeling to the fight against bacterial antibiotic resistance

Modeling the transmission of antibiotic-resistant Enterobacterales in the community: A systematic review

BACKGROUND

Antibiotic-resistant Enterobacterales (ARE) are a public health threat worldwide. Dissemination of these opportunistic pathogens has been largely studied in hospitals. Despite high prevalence of asymptomatic colonization in the community in some regions of the world, less is known about ARE acquisition and spread in this setting. As explaining the community ARE dynamics has not been straightforward, mathematical models can be key to explore underlying phenomena and further evaluate the impact of interventions to curb ARE circulation outside of hospitals.

METHODS

We conducted a systematic review of mathematical modeling studies focusing on the transmission of AR-E in the community, excluding models only specific to hospitals. We extracted model features (population, setting), formalism (compartmental, individual-based), biological hypotheses (transmission, infection, antibiotic impact, resistant strain specificities) and main findings. We discussed additional mechanisms to be considered, open scientific questions, and most pressing data needs.

RESULTS

We identified 18 modeling studies focusing on the human transmission of ARE in the community (n=11) or in both community and hospital (n=7). Models aimed at (i) understanding mechanisms driving resistance dynamics; (ii) identifying and quantifying transmission routes; or (iii) evaluating public health interventions to reduce resistance. To overcome the difficulty of reproducing observed ARE dynamics in the community using the classical two-strains competition model, studies proposed to include mechanisms such as within-host strain competition or a strong host population structure. Studies inferring model parameters from longitudinal carriage data were mostly based on models considering the ARE strain only. They showed differences in ARE carriage duration depending on the acquisition mode: returning travelers have a significantly shorter carriage duration than discharged hospitalized patient or healthy individuals. Interestingly, predictions across models regarding the success of public health interventions to reduce ARE rates depended on pathogens, settings, and antibiotic resistance mechanisms. For E. coli, reducing person-to-person transmission in the community had a stronger effect than reducing antibiotic use in the community. For Klebsiella pneumoniae, reducing antibiotic use in hospitals was more efficient than reducing community use.

CONCLUSIONS

This study raises the limited number of modeling studies specifically addressing the transmission of ARE in the community. It highlights the need for model development and community-based data collection especially in low- and middle-income countries to better understand acquisition routes and their relative contribution to observed ARE levels. Such modeling will be critical to correctly design and evaluate public health interventions to control ARE transmission in the community and further reduce the associated infection burden.

A stochastic analysis of the interplay between antibiotic dose, mode of action, and bacterial competition in the evolution of antibiotic resistance

The use of an antibiotic may lead to the emergence and spread of bacterial strains resistant to this antibiotic. Experimental and theoretical studies have investigated the drug dose that minimizes the risk of resistance evolution over the course of treatment of an individual, showing that the optimal dose will either be the highest or the lowest drug concentration possible to administer; however, no analytical results exist that help decide between these two extremes. To address this gap, we develop a stochastic mathematical model of bacterial dynamics under antibiotic treatment. We explore various scenarios of density regulation (bacterial density affects cell birth or death rates), and antibiotic modes of action (biostatic or biocidal). We derive analytical results for the survival probability of the resistant subpopulation until the end of treatment, the size of the resistant subpopulation at the end of treatment, the carriage time of the resistant subpopulation until it is replaced by a sensitive one after treatment, and we verify these results with stochastic simulations. We find that the scenario of density regulation and the drug mode of action are important determinants of the survival of a resistant subpopulation. Resistant cells survive best when bacterial competition reduces cell birth and under biocidal antibiotics. Compared to an analogous deterministic model, the population size reached by the resistant type is larger and carriage time is slightly reduced by stochastic loss of resistant cells. Moreover, we obtain an analytical prediction of the antibiotic concentration that maximizes the survival of resistant cells, which may help to decide which drug dosage (not) to administer. Our results are amenable to experimental tests and help link the within and between host scales in epidemiological models.

Challenges in Forecasting Antimicrobial Resistance

Antimicrobial resistance is a major threat to human health. Since the 2000s, computational tools for predicting infectious diseases have been greatly advanced; however, efforts to develop real-time forecasting models for antimicrobial-resistant organisms (AMROs) have been absent. In this perspective, we discuss the utility of AMRO forecasting at different scales, highlight the challenges in this field, and suggest future research priorities. We also discuss challenges in scientific understanding, access to high-quality data, model calibration, and implementation and evaluation of forecasting models. We further highlight the need to initiate research on AMRO forecasting using currently available data and resources to galvanize the research community and address initial practical questions.

Identification of the elements of models of antimicrobial resistance of bacteria for assessing their usefulness and usability in One Health decision making: a protocol for scoping review

INTRODUCTION

Antimicrobial resistance (AMR) is a complex problem that requires the One Health approach, that is, a collaboration among various disciplines working in different sectors (animal, human and environment) to resolve it. Mathematical and statistical models have been used to understand AMR development, emergence, dissemination, prediction and forecasting. A review of the published models of AMR will help consolidate our knowledge of the dynamics of AMR and will also facilitate decision-makers and researchers in evaluating the credibility, generalisability and interpretation of the results and aspects of AMR models. The study objective is to identify and synthesise knowledge on mathematical and statistical models of AMR among bacteria in animals, humans and environmental compartments.

METHODS AND ANALYSIS

Eligibility criteria: Original research studies reporting mathematical and statistical models of AMR among bacteria in animal, human and environmental compartments that were published until 2022 in English, French and Spanish will be included in this study.

SOURCES OF EVIDENCE

Database of PubMed, Agricola (Ovid), Centre for Agriculture and Bioscience Direct (CABI), Web of Science (Clarivate), Cumulative Index to Nursing and Allied Health Literature (CINAHL) and MathScinet. Data charting: Metadata of the study, the context of the study, model structure, model process and reporting quality will be extracted. A narrative summary of this information, gaps and recommendations will be prepared and reported in One Health decision-making context.

ETHICS AND DISSEMINATION

Research ethics board approval was not obtained for this study as neither human participation nor unpublished human data were used in this study. The study findings will be widely disseminated among the One Health Modelling Network for Emerging Infections network and stakeholders by means of conferences, and publication in open-access peer-reviewed journals.

Modeling the Impact of Management Changes on the Infection Dynamics of Extended-Spectrum Beta-Lactamase-Producing Escherichia coli in the Broiler Production

Livestock animals, especially poultry, are a known reservoir for extended-spectrum beta-lactamase (ESBL)-producing Escherichia coli (E. coli). They may enter the pen either via positive day-old chicks or via the environment. We developed a mathematical model to illustrate the entry and dissemination of resistant bacteria in a broiler pen during one fattening period in order to investigate the effectiveness of intervention measures on this infection process. Different management measures, such as varying amounts of litter, a slow-growing breed or lower stocking densities, were tested for their effects on broiler colonization. We also calculated the impact of products that may influence the microbiota in the chicks’ digestive tract, such as pre- or probiotics, feed supplements or competitive exclusion products. Our model outcomes show that a contaminated pen or positive chicks at the beginning of the fattening period can infect the entire flock. Increasing the amount of litter and decreasing the stocking density were shown to be effective in our model. Differences in the route of entry were found: if the chicks are already positive, the litter quantity must be increased to at least six times the standard of 1000 g/m2, whereas, if the pen is contaminated on the first day, three times the litter quantity is sufficient. A reduced stocking density of 20 kg/m2 had a significant effect on the incidence of infection only in a previously contaminated pen. Combinations of two or three measures were effective in both scenarios; similarly, feed additives may be beneficial in reducing the growth rate of ESBL-producing E. coli. This model is a valuable tool for evaluating interventions to reduce the transmission and spread of resistant bacteria in broiler houses. However, data are still needed to optimize the model, such as growth rates or survival data of ESBL-producing E. coli in different environments.

Microbiome-pathogen interactions drive epidemiological dynamics of antibiotic resistance: A modeling study applied to nosocomial pathogen control

The human microbiome can protect against colonization with pathogenic antibiotic-resistant bacteria (ARB), but its impacts on the spread of antibiotic resistance are poorly understood. We propose a mathematical modeling framework for ARB epidemiology formalizing within-host ARB-microbiome competition, and impacts of antibiotic consumption on microbiome function. Applied to the healthcare setting, we demonstrate a trade-off whereby antibiotics simultaneously clear bacterial pathogens and increase host susceptibility to their colonization, and compare this framework with a traditional strain-based approach. At the population level, microbiome interactions drive ARB incidence, but not resistance rates, reflecting distinct epidemiological relevance of different forces of competition. Simulating a range of public health interventions (contact precautions, antibiotic stewardship, microbiome recovery therapy) and pathogens (Clostridioides difficile, methicillin-resistant Staphylococcus aureus, multidrug-resistant Enterobacteriaceae) highlights how species-specific within-host ecological interactions drive intervention efficacy. We find limited impact of contact precautions for Enterobacteriaceae prevention, and a promising role for microbiome-targeted interventions to limit ARB spread.

Mixed effect modeling of tetracycline resistance levels in Danish slaughter pigs

Mathematical and statistical modeling can be a very useful tool in understanding and fighting antimicrobial resistance (AMR). Here we present investigations of mixed effect models of varying complexity in order to identify and address possible management factors affecting the tetracycline AMR levels in Danish pig farms. Besides antimicrobial exposure during pigs life cycle, the type of production seems to also have an influence. The results concludes that not only fully integrated farms (CHR integrated) but also farms in a production network with a single ownership (CVR integrated) might have a preventive effect on levels of tetracycline AMR compared to more complex trading patterns.

Drivers of ESBL-producing Escherichia coli dynamics in calf fattening farms: A modelling study

The contribution of bacteria in livestock to the global burden of antimicrobial resistance raises concerns worldwide. However, the dynamics of selection and diffusion of antimicrobial resistance in farm animals are not fully understood. Here, we used veal calf fattening farms as a model system, as they are a known reservoir of Extended Spectrum β-Lactamase-producing Escherichia coli (ESBL-EC). Longitudinal data of ESBL-EC carriage and antimicrobial use (AMU) were collected from three veal calf farms during the entire fattening process. We developed 18 agent-based mechanistic models to assess different hypotheses regarding the main drivers of ESBL-EC dynamics in calves. The models were independently fitted to the longitudinal data using Markov Chain Monte Carlo and the best model was selected. Within-farm transmission between individuals and sporadic events of contamination were found to drive ESBL-EC dynamics on farms. In the absence of AMU, the median carriage duration of ESBL-EC was estimated to be 19.6 days (95% credible interval: [12.7; 33.3]). In the best model, AMU was found to influence ESBL-EC dynamics, by affecting ESBL-EC clearance rather than acquisition. This effect of AMU was estimated to decrease gradually after the end of exposure and to disappear after 62.5 days [50.0; 76.9]. Moreover, using a simulation study, we quantified the efficacy of ESBL-EC mitigation strategies. Decreasing ESBL-EC prevalence by 50% on arrival at the fattening farm reduced prevalence at slaughter age by 33.3%. Completely eliminating the use of selective antibiotics on arrival had a strong effect on average ESBL-EC prevalence (relative reduction of 77.0%), but the effect was mild if this use was only decreased by 50% compared to baseline (relative reduction of 3.3%).

Leveraging Computational Modeling to Understand Infectious Diseases

Purpose of Review

Computational and mathematical modeling have become a critical part of understanding in-host infectious disease dynamics and predicting effective treatments. In this review, we discuss recent findings pertaining to the biological mechanisms underlying infectious diseases, including etiology, pathogenesis, and the cellular interactions with infectious agents. We present advances in modeling techniques that have led to fundamental disease discoveries and impacted clinical translation.

Recent Findings

Combining mechanistic models and machine learning algorithms has led to improvements in the treatment of Shigella and tuberculosis through the development of novel compounds. Modeling of the epidemic dynamics of malaria at the within-host and between-host level has afforded the development of more effective vaccination and antimalarial therapies. Similarly, in-host and host-host models have supported the development of new HIV treatment modalities and an improved understanding of the immune involvement in influenza. In addition, large-scale transmission models of SARS-CoV-2 have furthered the understanding of coronavirus disease and allowed for rapid policy implementations on travel restrictions and contract tracing apps.

Summary

Computational modeling is now more than ever at the forefront of infectious disease research due to the COVID-19 pandemic. This review highlights how infectious diseases can be better understood by connecting scientists from medicine and molecular biology with those in computer science and applied mathematics.

Population structure across scales facilitates coexistence and spatial heterogeneity of antibiotic-resistant infections

Antibiotic-resistant infections are a growing threat to human health, but basic features of the eco-evolutionary dynamics remain unexplained. Most prominently, there is no clear mechanism for the long-term coexistence of both drug-sensitive and resistant strains at intermediate levels, a ubiquitous pattern seen in surveillance data. Here we show that accounting for structured or spatially-heterogeneous host populations and variability in antibiotic consumption can lead to persistent coexistence over a wide range of treatment coverages, drug efficacies, costs of resistance, and mixing patterns. Moreover, this mechanism can explain other puzzling spatiotemporal features of drug-resistance epidemiology that have received less attention, such as large differences in the prevalence of resistance between geographical regions with similar antibiotic consumption or that neighbor one another. We find that the same amount of antibiotic use can lead to very different levels of resistance depending on how treatment is distributed in a transmission network. We also identify parameter regimes in which population structure alone cannot support coexistence, suggesting the need for other mechanisms to explain the epidemiology of antibiotic resistance. Our analysis identifies key features of host population structure that can be used to assess resistance risk and highlights the need to include spatial or demographic heterogeneity in models to guide resistance management.

Simulation models for transmission of health care-associated infection: A systematic review

BACKGROUND

Health care-associated infections (HAIs) are a global health burden because of their significant impact on patient health and health care systems. Mechanistic simulation modeling that captures the dynamics between patients, pathogens, and the environment is increasingly being used to improve understanding of epidemiological patterns of HAIs and to facilitate decisions on infection prevention and control (IPC). The purpose of this review is to present a systematic review to establish (1) how simulation models have been used to investigate HAIs and their mitigation and (2) how these models have evolved over time, as well as identify (3) gaps in their adoption and (4) useful directions for their future development.

METHODS

The review involved a systematic search and identification of studies using system dynamics, discrete event simulation, and agent-based model to study HAIs.

RESULTS

The complexity of simulation models developed for HAIs significantly increased but heavily concentrated on transmission dynamics of methicillin-resistant Staphylococcus aureus in the hospitals of high-income countries. Neither HAIs in other health care settings, the influence of contact networks within a health care facility, nor patient sharing and referring networks across health care settings were sufficiently understood.

CONCLUSIONS

This systematic review provides a broader overview of existing simulation models in HAIs to identify the gaps and to direct and facilitate further development of appropriate models in this emerging field.

Utilising sigmoid models to predict the spread of antimicrobial resistance at the country level

BackgroundThe spread of antimicrobial resistance (AMR) is of worldwide concern. Public health policymakers and pharmaceutical companies pursuing antibiotic development require accurate predictions about the future spread of AMR.AimWe aimed to identify and model temporal and geographical patterns of AMR spread and to predict future trends based on a slow, intermediate or rapid rise in resistance.MethodsWe obtained data from five antibiotic resistance surveillance projects spanning the years 1997 to 2015. We aggregated the isolate-level or country-level data by country and year to produce country-bacterium-antibiotic class triads. We fitted both linear and sigmoid models to these triads and chose the one with the better fit. For triads that conformed to a sigmoid model, we classified AMR progression into one of three characterising paces: slow, intermediate or fast, based on the sigmoid slope. Within each pace category, average sigmoid models were calculated and validated.ResultsWe constructed a database with 51,670 country-year-bacterium-antibiotic observations, grouped into 7,440 country-bacterium-antibiotic triads. A total of 1,037 triads (14%) met the inclusion criteria. Of these, 326 (31.4%) followed a sigmoid (logistic) pattern over time. Among 107 triads for which both sigmoid and linear models could be fit, the sigmoid model was a better fit in 84%. The sigmoid model deviated from observed data by a median of 6.5%; the degree of deviation was related to the pace of spread.ConclusionWe present a novel method of describing and predicting the spread of antibiotic-resistant organisms.

The effect of spatiotemporal antibiotic inhomogeneities on the evolution of resistance

Combating the evolution of widespread antibiotic resistance is one of the most pressing challenges facing modern medicine. Recent research has demonstrated that the evolution of pathogens with high levels of resistance can be accelerated by spatial and temporal inhomogeneities in antibiotic concentration, which frequently arise in patients and the environment. Strategies to predict and counteract the effects of such inhomogeneities will be critical in the fight against resistance. In this paper we develop a mechanistic framework for modelling the adaptive evolution of resistance in the presence of spatiotemporal antibiotic concentrations, which treats the adaptive process as an interaction between two mutually orthogonal forces; the first returns cells to their wild-type state in the absence of antibiotic selection, and the second selects for increased coping ability in the presence of an antibiotic. We apply our model to investigate laboratory adaptation experiments, and then extend it to consider the case in which multiple strategies for resistance undergo competitive evolution.

Addressing the Unknowns of Antimicrobial Resistance: Quantifying and Mapping the Drivers of Burden

The global threat of antimicrobial resistance (AMR) has arisen through a network of complex interacting factors. Many different sources and transmission pathways contribute to the ever-growing burden of AMR in our clinical settings. The lack of data on these mechanisms and the relative importance of different factors causing the emergence and spread of AMR hampers our global efforts to effectively manage the risks. Importantly, we have little quantitative knowledge on the relative contributions of these sources and are likely to be targeting our interventions suboptimally as a result. Here we propose a systems mapping approach to address the urgent need for reliable and timely data to strengthen the response to AMR.

Mathematical modelling to study the horizontal transfer of antimicrobial resistance genes in bacteria: current state of the field and recommendations

Antimicrobial resistance (AMR) is one of the greatest public health challenges we are currently facing. To develop effective interventions against this, it is essential to understand the processes behind the spread of AMR. These are partly dependent on the dynamics of horizontal transfer of resistance genes between bacteria, which can occur by conjugation (direct contact), transformation (uptake from the environment) or transduction (mediated by bacteriophages). Mathematical modelling is a powerful tool to investigate the dynamics of AMR; however, the extent of its use to study the horizontal transfer of AMR genes is currently unclear. In this systematic review, we searched for mathematical modelling studies that focused on horizontal transfer of AMR genes. We compared their aims and methods using a list of predetermined criteria and used our results to assess the current state of this research field. Of the 43 studies we identified, most focused on the transfer of single genes by conjugation in Escherichia coli in culture and its impact on the bacterial evolutionary dynamics. Our findings highlight the existence of an important research gap in the dynamics of transformation and transduction and the overall public health implications of horizontal transfer of AMR genes. To further develop this field and improve our ability to control AMR, it is essential that we clarify the structural complexity required to study the dynamics of horizontal gene transfer, which will require cooperation between microbiologists and modellers.

Population-level mathematical modeling of antimicrobial resistance: a systematic review

BACKGROUND

Mathematical transmission models are increasingly used to guide public health interventions for infectious diseases, particularly in the context of emerging pathogens; however, the contribution of modeling to the growing issue of antimicrobial resistance (AMR) remains unclear. Here, we systematically evaluate publications on population-level transmission models of AMR over a recent period (2006-2016) to gauge the state of research and identify gaps warranting further work.

METHODS

We performed a systematic literature search of relevant databases to identify transmission studies of AMR in viral, bacterial, and parasitic disease systems. We analyzed the temporal, geographic, and subject matter trends, described the predominant medical and behavioral interventions studied, and identified central findings relating to key pathogens.

RESULTS

We identified 273 modeling studies; the majority of which (> 70%) focused on 5 infectious diseases (human immunodeficiency virus (HIV), influenza virus, Plasmodium falciparum (malaria), Mycobacterium tuberculosis (TB), and methicillin-resistant Staphylococcus aureus (MRSA)). AMR studies of influenza and nosocomial pathogens were mainly set in industrialized nations, while HIV, TB, and malaria studies were heavily skewed towards developing countries. The majority of articles focused on AMR exclusively in humans (89%), either in community (58%) or healthcare (27%) settings. Model systems were largely compartmental (76%) and deterministic (66%). Only 43% of models were calibrated against epidemiological data, and few were validated against out-of-sample datasets (14%). The interventions considered were primarily the impact of different drug regimens, hygiene and infection control measures, screening, and diagnostics, while few studies addressed de novo resistance, vaccination strategies, economic, or behavioral changes to reduce antibiotic use in humans and animals.

CONCLUSIONS

The AMR modeling literature concentrates on disease systems where resistance has been long-established, while few studies pro-actively address recent rise in resistance in new pathogens or explore upstream strategies to reduce overall antibiotic consumption. Notable gaps include research on emerging resistance in Enterobacteriaceae and Neisseria gonorrhoeae; AMR transmission at the animal-human interface, particularly in agricultural and veterinary settings; transmission between hospitals and the community; the role of environmental factors in AMR transmission; and the potential of vaccines to combat AMR.

Modelling environmental antibiotic-resistance gene abundance: A meta-analysis

The successful treatment of infectious diseases heavily relies on the therapeutic usage of antibiotics. However, the high use of antibiotics in humans and animals leads to increasing pressure on bacterial populations in favour of resistant phenotypes. Antibiotics reach the environment from a variety of emission sources and are being detected at relatively low concentrations. Given the possibility of selective pressure to occur at sub-inhibitory concentrations, the ecological impact of environmental antibiotic levels on microbial communities and resistance levels is vastly unknown. Quantification of antibiotic-resistance genes (ARG) and of antibiotic concentrations is becoming commonplace. Yet, these two parameters are often assessed separately and in a specific spatiotemporal context, thus missing the opportunity to investigate how antibiotics and ARGs relate. Furthermore, antibiotic (multi)resistance has been receiving ever growing attention from researchers, policy-makers, businesses and civil society. Our aim was to collect the limited data on antibiotic concentrations and ARG abundance currently available to explore if a relationship could be defined in surface waters, sediments and wastewaters. A metric of antibiotic selective pressure, i.e. the sum of concentrations corrected for microbial inhibition potency, was used to correlate the presence of antibiotics in the environment to total relative abundance of ARG while controlling for basic sources of non-independent variability, such as country, year, study, sample and antibiotic class. The results of this meta-analysis show a significant statistical effect of antibiotic pressure and type of environmental compartment on the increase of ARG abundance even at very low levels. If global environmental antibiotic pollution continues, ARG abundance is expected to continue as well. Moreover, our analysis emphasizes the importance of integrating existing information particularly when attempting to describe complex relationships with limited mechanistic understanding.

Evolutionary epidemiology models to predict the dynamics of antibiotic resistance

The evolution of resistance to antibiotics is a major public health problem and an example of rapid adaptation under natural selection by antibiotics. The dynamics of antibiotic resistance within and between hosts can be understood in the light of mathematical models that describe the epidemiology and evolution of the bacterial population. "Between-host" models describe the spread of resistance in the host community, and in more specific settings such as hospitalized hosts (treated by antibiotics at a high rate), or farm animals. These models make predictions on the best strategies to limit the spread of resistance, such as reducing transmission or adapting the prescription of several antibiotics. Models can be fitted to epidemiological data in the context of intensive care units or hospitals to predict the impact of interventions on resistance. It has proven harder to explain the dynamics of resistance in the community at large, in particular because models often do not reproduce the observed coexistence of drug-sensitive and drug-resistant strains. "Within-host" models describe the evolution of resistance within the treated host. They show that the risk of resistance emergence is maximal at an intermediate antibiotic dose, and some models successfully explain experimental data. New models that include the complex host population structure, the interaction between resistance-determining loci and other loci, or integrating the within- and between-host levels will allow better interpretation of epidemiological and genomic data from common pathogens and better prediction of the evolution of resistance.

Inference and control of the nosocomial transmission of methicillin-resistant Staphylococcus aureus

Methicillin-resistant Staphylococcus aureus (MRSA) is a continued threat to human health in both community and healthcare settings. In hospitals, control efforts would benefit from accurate estimation of asymptomatic colonization and infection importation rates from the community. However, developing such estimates remains challenging due to limited observation of colonization and complicated transmission dynamics within hospitals and the community. Here, we develop an inference framework that can estimate these key quantities by combining statistical filtering techniques, an agent-based model, and real-world patient-to-patient contact networks, and use this framework to infer nosocomial transmission and infection importation over an outbreak spanning 6 years in 66 Swedish hospitals. In particular, we identify a small number of patients with disproportionately high risk of colonization. In retrospective control experiments, interventions targeted to these individuals yield a substantial improvement over heuristic strategies informed by number of contacts, length of stay and contact tracing.

Send more data: a systematic review of mathematical models of antimicrobial resistance

Background

Antimicrobial resistance is a global health problem that demands all possible means to control it. Mathematical modelling is a valuable tool for understanding the mechanisms of AMR development and spread, and can help us to investigate and propose novel control strategies. However, it is of vital importance that mathematical models have a broad utility, which can be assured if good modelling practice is followed.

Objective

The objective of this study was to provide a comprehensive systematic review of published models of AMR development and spread. Furthermore, the study aimed to identify gaps in the knowledge required to develop useful models.

Methods

The review comprised a comprehensive literature search with 38 selected studies. Information was extracted from the selected papers using an adaptation of previously published frameworks, and was evaluated using the TRACE good modelling practice guidelines.

Results

None of the selected papers fulfilled the TRACE guidelines. We recommend that future mathematical models should: a) model the biological processes mechanistically, b) incorporate uncertainty and variability in the system using stochastic modelling, c) include a sensitivity analysis and model external and internal validation.

Conclusion

Many mathematical models of AMR development and spread exist. There is still a lack of knowledge about antimicrobial resistance, which restricts the development of useful mathematical models.

Quantifying where human acquisition of antibiotic resistance occurs: a mathematical modelling study

BACKGROUND

Antibiotic-resistant bacteria (ARB) are selected by the use of antibiotics. The rational design of interventions to reduce levels of antibiotic resistance requires a greater understanding of how and where ARB are acquired. Our aim was to determine whether acquisition of ARB occurs more often in the community or hospital setting.

METHODS

We used a mathematical model of the natural history of ARB to estimate how many ARB were acquired in each of these two environments, as well as to determine key parameters for further investigation. To do this, we explored a range of realistic parameter combinations and considered a case study of parameters for an important subset of resistant strains in England.

RESULTS

If we consider all people with ARB in the total population (community and hospital), the majority, under most clinically derived parameter combinations, acquired their resistance in the community, despite higher levels of antibiotic use and transmission of ARB in the hospital. However, if we focus on just the hospital population, under most parameter combinations a greater proportion of this population acquired ARB in the hospital.

CONCLUSIONS

It is likely that the majority of ARB are being acquired in the community, suggesting that efforts to reduce overall ARB carriage should focus on reducing antibiotic usage and transmission in the community setting. However, our framework highlights the need for better pathogen-specific data on antibiotic exposure, ARB clearance and transmission parameters, as well as the link between carriage of ARB and health impact. This is important to determine whether interventions should target total ARB carriage or hospital-acquired ARB carriage, as the latter often dominated in hospital populations.

Application of dynamic modelling techniques to the problem of antibacterial use and resistance: a scoping review

Selective pressure exerted by the widespread use of antibacterial drugs is accelerating the development of resistant bacterial populations. The purpose of this scoping review was to summarise the range of studies that use dynamic models to analyse the problem of bacterial resistance in relation to antibacterial use in human and animal populations. A comprehensive search of the peer-reviewed literature was performed and non-duplicate articles (n = 1486) were screened in several stages. Charting questions were used to extract information from the articles included in the final subset (n = 81). Most studies (86%) represent the system of interest with an aggregate model; individual-based models are constructed in only seven articles. There are few examples of inter-host models outside of human healthcare (41%) and community settings (38%). Resistance is modelled for a non-specific bacterial organism and/or antibiotic in 40% and 74% of the included articles, respectively. Interventions with implications for antibacterial use were investigated in 67 articles and included changes to total antibiotic consumption, strategies for drug management and shifts in category/class use. The quality of documentation related to model assumptions and uncertainty varies considerably across this subset of articles. There is substantial room to improve the transparency of reporting in the antibacterial resistance modelling literature as is recommended by best practice guidelines.

Emergence and selection of isoniazid and rifampin resistance in tuberculosis granulomas

Drug resistant tuberculosis is increasing world-wide. Resistance against isoniazid (INH), rifampicin (RIF), or both (multi-drug resistant TB, MDR-TB) is of particular concern, since INH and RIF form part of the standard regimen for TB disease. While it is known that suboptimal treatment can lead to resistance, it remains unclear how host immune responses and antibiotic dynamics within granulomas (sites of infection) affect emergence and selection of drug-resistant bacteria. We take a systems pharmacology approach to explore resistance dynamics within granulomas. We integrate spatio-temporal host immunity, INH and RIF dynamics, and bacterial dynamics (including fitness costs and compensatory mutations) in a computational framework. We simulate resistance emergence in the absence of treatment, as well as resistance selection during INH and/or RIF treatment. There are four main findings. First, in the absence of treatment, the percentage of granulomas containing resistant bacteria mirrors the non-monotonic bacterial dynamics within granulomas. Second, drug-resistant bacteria are less frequently found in non-replicating states in caseum, compared to drug-sensitive bacteria. Third, due to a steeper dose response curve and faster plasma clearance of INH compared to RIF, INH-resistant bacteria have a stronger influence on treatment outcomes than RIF-resistant bacteria. Finally, under combination therapy with INH and RIF, few MDR bacteria are able to significantly affect treatment outcomes. Overall, our approach allows drug-specific prediction of drug resistance emergence and selection in the complex granuloma context. Since our predictions are based on pre-clinical data, our approach can be implemented relatively early in the treatment development process, thereby enabling pro-active rather than reactive responses to emerging drug resistance for new drugs. Furthermore, this quantitative and drug-specific approach can help identify drug-specific properties that influence resistance and use this information to design treatment regimens that minimize resistance selection and expand the useful life-span of new antibiotics.

Vaccination can drive an increase in frequencies of antibiotic resistance among nonvaccine serotypes of Streptococcus pneumoniae

The bacterial pathogen Streptococcus pneumoniae is a major public health concern, being responsible for more than 1.5 million deaths annually through pneumonia, meningitis, and septicemia. Available vaccines target only a subset of serotypes, so vaccination is often accompanied by a rise in the frequency of nonvaccine serotypes. Epidemiological studies suggest that such a change in serotype frequencies is often coupled with an increase of antibiotic resistance among nonvaccine serotypes. Building on previous multilocus models for bacterial pathogen population structure, we have developed a theoretical framework incorporating variation of serotype and antibiotic resistance to examine how their associations may be affected by vaccination. Using this framework, we find that vaccination can result in a rapid increase in the frequency of preexisting resistant variants of nonvaccine serotypes due to the removal of competition from vaccine serotypes.

Modeling the Emergence of Antibiotic Resistance in the Environment: an Analytical Solution for the Minimum Selection Concentration

Environmental antibiotic risk management requires an understanding of how subinhibitory antibiotic concentrations contribute to the spread of resistance. We develop a simple model of competition between sensitive and resistant bacterial strains to predict the minimum selection concentration (MSC), the lowest level of antibiotic at which resistant bacteria are selected. We present an analytical solution for the MSC based on the routinely measured MIC, the selection coefficient (sc) that expresses fitness differences between strains, the intrinsic net growth rate, and the shape of the bacterial growth dose-response curve with antibiotic or metal exposure (the Hill coefficient [κ]). We calibrated the model by optimizing the Hill coefficient to fit previously reported experimental growth rate difference data. The model fit varied among nine compound-taxon combinations examined but predicted the experimentally observed MSC/MIC ratio well (R² ≥ 0.95). The shape of the antibiotic response curve varied among compounds (0.7 ≤ κ ≤ 10.5), with the steepest curve being found for the aminoglycosides streptomycin and kanamycin. The model was sensitive to this antibiotic response curve shape and to the sc, indicating the importance of fitness differences between strains for determining the MSC. The MSC can be >1 order of magnitude lower than the MIC, typically by the factor sc^κ This study provides an initial quantitative depiction and a framework for a research agenda to examine the growing evidence of selection for resistant bacterial communities at low environmental antibiotic concentrations.

In silico analysis of antibiotic-induced Clostridium difficile infection: Remediation techniques and biological adaptations

In this paper we study antibiotic-induced C. difficile infection (CDI), caused by the toxin-producing C. difficile (CD), and implement clinically-inspired simulated treatments in a computational framework that synthesizes a generalized Lotka-Volterra (gLV) model with SIR modeling techniques. The gLV model uses parameters derived from an experimental mouse model, in which the mice are administered antibiotics and subsequently dosed with CD. We numerically identify which of the experimentally measured initial conditions are vulnerable to CD colonization, then formalize the notion of CD susceptibility analytically. We simulate fecal transplantation, a clinically successful treatment for CDI, and discover that both the transplant timing and transplant donor are relevant to the the efficacy of the treatment, a result which has clinical implications. We incorporate two nongeneric yet dangerous attributes of CD into the gLV model, sporulation and antibiotic-resistant mutation, and for each identify relevant SIR techniques that describe the desired attribute. Finally, we rely on the results of our framework to analyze an experimental study of fecal transplants in mice, and are able to explain observed experimental results, validate our simulated results, and suggest model-motivated experiments.

Mathematical models of infection transmission in healthcare settings: recent advances from the use of network structured data

PURPOSE OF REVIEW

Mathematical modeling approaches have brought important contributions to the study of pathogen spread in healthcare settings over the last 20 years. Here, we conduct a comprehensive systematic review of mathematical models of disease transmission in healthcare settings and assess the application of contact and patient transfer network data over time and their impact on our understanding of transmission dynamics of infections.

RECENT FINDINGS

Recently, with the increasing availability of data on the structure of interindividual and interinstitution networks, models incorporating this type of information have been proposed, with the aim of providing more realistic predictions of disease transmission in healthcare settings. Models incorporating realistic data on individual or facility networks often remain limited to a few settings and a few pathogens (mostly methicillin-resistant Staphylococcus aureus).

SUMMARY

To respond to the objectives of creating improved infection prevention and control measures and better understanding of healthcare-associated infections transmission dynamics, further innovations in data collection and parameter estimation in modeling is required.

Spread of hospital-acquired infections: A comparison of healthcare networks

Hospital-acquired infections (HAIs), including emerging multi-drug resistant organisms, threaten healthcare systems worldwide. Efficient containment measures of HAIs must mobilize the entire healthcare network. Thus, to best understand how to reduce the potential scale of HAI epidemic spread, we explore patient transfer patterns in the French healthcare system. Using an exhaustive database of all hospital discharge summaries in France in 2014, we construct and analyze three patient networks based on the following: transfers of patients with HAI (HAI-specific network); patients with suspected HAI (suspected-HAI network); and all patients (general network). All three networks have heterogeneous patient flow and demonstrate small-world and scale-free characteristics. Patient populations that comprise these networks are also heterogeneous in their movement patterns. Ranking of hospitals by centrality measures and comparing community clustering using community detection algorithms shows that despite the differences in patient population, the HAI-specific and suspected-HAI networks rely on the same underlying structure as that of the general network. As a result, the general network may be more reliable in studying potential spread of HAIs. Finally, we identify transfer patterns at both the French regional and departmental (county) levels that are important in the identification of key hospital centers, patient flow trajectories, and regional clusters that may serve as a basis for novel wide-scale infection control strategies.

Hospital-acquired infections (HAIs), including emerging multi-drug resistant organisms, threaten healthcare systems worldwide. Efficient containment measures of HAIs must mobilize the entire healthcare network. Thus, to best understand how to reduce the scale of potential HAI epidemic spread, we explore patient transfer patterns in the French healthcare system. We construct and compare the characteristics of three different patient transfer networks based on data on transfers of patients with diagnosed HAIs, suspected HAIs, or of all patients. Our analyses show that these healthcare networks, the patient populations that comprise them and the patient movement patterns are heterogeneous and centralized. Despite the differences in patient populations, the HAI-specific and suspected-HAI healthcare networks have the same underlying structure as that of the general healthcare network. We identify key hospital centers, patient flow trajectories, at both the regional and department (county) level that may serve as a basis for proposing novel wide-scale infection control strategies.

Benefits and unintended consequences of antimicrobial de-escalation: Implications for stewardship programs

Sequential antimicrobial de-escalation aims to minimize resistance to high-value broad-spectrum empiric antimicrobials by switching to alternative drugs when testing confirms susceptibility. Though widely practiced, the effects de-escalation are not well understood. Definitions of interventions and outcomes differ among studies. We use mathematical models of the transmission and evolution of Pseudomonas aeruginosa in an intensive care unit to assess the effect of de-escalation on a broad range of outcomes, and clarify expectations. In these models, de-escalation reduces the use of high-value drugs and preserves the effectiveness of empiric therapy, while also selecting for multidrug-resistant strains and leaving patients vulnerable to colonization and superinfection. The net effect of de-escalation in our models is to increase infection prevalence while also increasing the probability of effective treatment. Changes in mortality are small, and can be either positive or negative. The clinical significance of small changes in outcomes such as infection prevalence and death may exceed more easily detectable changes in drug use and resistance. Integrating harms and benefits into ranked outcomes for each patient may provide a way forward in the analysis of these tradeoffs. Our models provide a conceptual framework for the collection and interpretation of evidence needed to inform antimicrobial stewardship.

Understanding the Impact of Interventions to Prevent Antimicrobial Resistant Infections in the Long-Term Care Facility: A Review and Practical Guide to Mathematical Modeling

OBJECTIVES (1) To systematically search for all dynamic mathematical models of infectious disease transmission in long-term care facilities (LTCFs); (2) to critically evaluate models of interventions against antimicrobial resistance (AMR) in this setting; and (3) to develop a checklist for hospital epidemiologists and policy makers by which to distinguish good quality models of AMR in LTCFs. METHODS The CINAHL, EMBASE, Global Health, MEDLINE, and Scopus databases were systematically searched for studies of dynamic mathematical models set in LTCFs. Models of interventions targeting methicillin-resistant Staphylococcus aureus in LTCFs were critically assessed. Using this analysis, we developed a checklist for good quality mathematical models of AMR in LTCFs. RESULTS AND DISCUSSION Overall, 18 papers described mathematical models that characterized the spread of infectious diseases in LTCFs, but no models of AMR in gram-negative bacteria in this setting were described. Future models of AMR in LTCFs require a more robust methodology (ie, formal model fitting to data and validation), greater transparency regarding model assumptions, setting-specific data, realistic and current setting-specific parameters, and inclusion of movement dynamics between LTCFs and hospitals. CONCLUSIONS Mathematical models of AMR in gram-negative bacteria in the LTCF setting, where these bacteria are increasingly becoming prevalent, are needed to help guide infection prevention and control. Improvements are required to develop outputs of sufficient quality to help guide interventions and policy in the future. We suggest a checklist of criteria to be used as a practical guide to determine whether a model is robust enough to test policy. Infect Control Hosp Epidemiol 2017;38:216-225.

Mathematical analysis of multi-antibiotic resistance

BACKGROUND

Multi-antibiotic resistance in bacterial infections is a growing threat to public health. Some experiments were carried out to study the multi-antibiotic resistance.

METHODS

The changes of the multi-antibiotic resistance with time were achieved by numerical simulations and the mathematical models, with the calculated temperature field, velocity field, and the antibiotic concentration field.

RESULTS

The computed results and experimental results are compared.

CONCLUSIONS

Both numerical simulations and the analytic models suggest that minor low concentrations of antibiotics could induce antibiotic resistance in bacteria.

Modeling the growth dynamics of multiple Escherichia coli strains in the pig intestine following intramuscular ampicillin treatment

Background

This study evaluated how dosing regimen for intramuscularly-administered ampicillin, composition of Escherichia coli strains with regard to ampicillin susceptibility, and excretion of bacteria from the intestine affected the level of resistance among Escherichia coli strains in the intestine of nursery pigs. It also examined the dynamics of the composition of bacterial strains during and after the treatment. The growth responses of strains to ampicillin concentrations were determined using in vitro growth curves. Using these results as input data, growth predictions were generated using a mathematical model to simulate the competitive growth of E. coli strains in a pig intestine under specified plasma concentration profiles of ampicillin.

Results

In vitro growth results demonstrated that the resistant strains did not carry a fitness cost for their resistance, and that the most susceptible strains were more affected by increasing concentrations of antibiotics that the rest of the strains. The modeling revealed that short treatment duration resulted in lower levels of resistance and that dosing frequency did not substantially influence the growth of resistant strains. Resistance levels were found to be sensitive to the number of competing strains, and this effect was enhanced by longer duration of treatment. High excretion of bacteria from the intestine favored resistant strains over sensitive strains, but at the same time it resulted in a faster return to pre-treatment levels after the treatment ended. When the duration of high excretion was set to be limited to the treatment time (i.e. the treatment was assumed to result in a cure of diarrhea) resistant strains required longer time to reach the previous level.

Conclusion

No fitness cost was found to be associated with ampicillin resistance in E. coli. Besides dosing factors, epidemiological factors (such as number of competing strains and bacterial excretion) influenced resistance development and need to be considered further in relation to optimal treatment strategies. The modeling approach used in the study is generic, and could be used for prediction of the effect of treatment with other drugs and other administration routes for effect on resistance development in the intestine of pigs.

Electronic supplementary material

The online version of this article (doi:10.1186/s12866-016-0823-3) contains supplementary material, which is available to authorized users.

Research Methods in Healthcare Epidemiology and Antimicrobial Stewardship-Mathematical Modeling

Mathematical modeling is a valuable methodology used to study healthcare epidemiology and antimicrobial stewardship, particularly when more traditional study approaches are infeasible, unethical, costly, or time consuming. We focus on 2 of the most common types of mathematical modeling, namely compartmental modeling and agent-based modeling, which provide important advantages-such as shorter developmental timelines and opportunities for extensive experimentation-over observational and experimental approaches. We summarize these advantages and disadvantages via specific examples and highlight recent advances in the methodology. A checklist is provided to serve as a guideline in the development of mathematical models in healthcare epidemiology and antimicrobial stewardship. Infect Control Hosp Epidemiol 2016;1-7.

Mathematical modelling of bacterial resistance to multiple antibiotics and immune system response

Resistance of developed bacteria to antibiotic treatment is a very important issue, because introduction of any new antibiotic is after a little while followed by the formation of resistant bacterial isolates in the clinic. The significant increase in clinical resistance to antibiotics is a troubling situation especially in nosocomial infections, where already defenseless patients can be unsuccessful to respond to treatment, causing even greater health issue. Nosocomial infections can be identified as those happening within 2 days of hospital acceptance, 3 days of discharge or 1 month of an operation. They influence 1 out of 10 patients admitted to hospital. Annually, this outcomes in 5000 deaths only in UK with a cost to the National Health Service of a billion pounds. Despite these problems, antibiotic therapy is still the most common method used to treat bacterial infections. On the other hand, it is often mentioned that immune system plays a major role in the progress of infections. In this context, we proposed a mathematical model defining population dynamics of both the specific immune cells produced according to the properties of bacteria by host and the bacteria exposed to multiple antibiotics synchronically, presuming that resistance is gained through mutations due to exposure to antibiotic. Qualitative analysis found out infection-free equilibrium point and other equilibrium points where resistant bacteria and immune system cells exist, only resistant bacteria exists and sensitive bacteria, resistant bacteria and immune system cells exist. As a result of this analysis, our model highlights the fact that when an individual’s immune system weakens, he/she suffers more from the bacterial infections which are believed to have been confined or terminated. Also, these results was supported by numerical simulations.

Population Dynamics of Patients with Bacterial Resistance in Hospital Environment

During the past decades, the increase of antibiotic resistance has become a major concern worldwide. The researchers found that superbugs with new type of resistance genes (NDM-1) have two aspects of transmission characteristics; the first is that the antibiotic resistance genes can horizontally transfer among bacteria, and the other is that the superbugs can spread between humans through direct contact. Based on these two transmission mechanisms, we study the dynamics of population in hospital environment where superbugs exist. In this paper, we build three mathematic models to illustrate the dynamics of patients with bacterial resistance in hospital environment. The models are analyzed using stability theory of differential equations. Positive equilibrium points of the system are investigated and their stability analysis is carried out. Moreover, the numerical simulation of the proposed model is also performed which supports the theoretical findings.

Application of PK/PD Modeling in Veterinary Field: Dose Optimization and Drug Resistance Prediction

Among veterinary drugs, antibiotics are frequently used. The true mean of antibiotic treatment is to administer dose of drug that will have enough high possibility of attaining the preferred curative effect, with adequately low chance of concentration associated toxicity. Rising of antibacterial resistance and lack of novel antibiotic is a global crisis; therefore there is an urgent need to overcome this problem. Inappropriate antibiotic selection, group treatment, and suboptimal dosing are mostly responsible for the mentioned problem. One approach to minimizing the antibacterial resistance is to optimize the dosage regimen. PK/PD model is important realm to be used for that purpose from several years. PK/PD model describes the relationship between drug potency, microorganism exposed to drug, and the effect observed. Proper use of the most modern PK/PD modeling approaches in veterinary medicine can optimize the dosage for patient, which in turn reduce toxicity and reduce the emergence of resistance. The aim of this review is to look at the existing state and application of PK/PD in veterinary medicine based on in vitro, in vivo, healthy, and disease model.

Pharmacodynamic modelling of in vitro activity of tetracycline against a representative, naturally occurring population of porcine Escherichia coli

Background

The complex relationship between drug concentrations and bacterial growth rates require not only the minimum inhibitory concentration but also other parameters to capture the dynamic nature of the relationship. To analyse this relationship between tetracycline concentration and growth of Escherichia coli representative of those found in the Danish pig population, we compared the growth of 50 randomly selected strains. The observed net growth rates were used to describe the in vitro pharmacodynamic relationship between drug concentration and net growth rate based on E_max model with three parameters: maximum net growth rate (α_max); concentration for a half-maximal response (E_max); and the Hill coefficient (γ).

Results

The net growth rate in the absence of antibiotic did not differ between susceptible and resistant isolates (P = 0.97). The net growth rate decreased with increasing tetracycline concentrations, and this decline was greater in susceptible strains than resistant strains. The lag phase, defined as the time needed for the strain to reach an OD₆₀₀ value of 0.01, increased exponentially with increasing tetracycline concentration. The pharmacodynamic parameters confirmed that the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \alpha_{max} $$\end{document}αmax between susceptible and resistant strains in the absence of a drug was not different. EC₅₀ increased linearly with MIC on a log–log scale, and γ was different between susceptible and resistant strains.

Conclusions

The in vitro model parameters described the inhibition effect of tetracycline on E. coli when strains were exposed to a wide range of tetracycline concentrations. These parameters, along with in vivo pharmacokinetic data, may be useful in mathematical models to predict in vivo competitive growth of many different strains and for development of optimal dosing regimens for preventing selection of resistance.

What should be considered if you decide to build your own mathematical model for predicting the development of bacterial resistance? Recommendations based on a systematic review of the literature

Acquired bacterial resistance is one of the causes of mortality and morbidity from infectious diseases. Mathematical modeling allows us to predict the spread of resistance and to some extent to control its dynamics. The purpose of this review was to examine existing mathematical models in order to understand the pros and cons of currently used approaches and to build our own model. During the analysis, seven articles on mathematical approaches to studying resistance that satisfied the inclusion/exclusion criteria were selected. All models were classified according to the approach used to study resistance in the presence of an antibiotic and were analyzed in terms of our research. Some models require modifications due to the specifics of the research. The plan for further work on model building is as follows: modify some models, according to our research, check all obtained models against our data, and select the optimal model or models with the best quality of prediction. After that we would be able to build a model for the development of resistance using the obtained results.

Pharmacokinetic-pharmacodynamic model to evaluate intramuscular tetracycline treatment protocols to prevent antimicrobial resistance in pigs

High instances of antimicrobial resistance are linked to both routine and excessive antimicrobial use, but excessive or inappropriate use represents an unnecessary risk. The competitive growth advantages of resistant bacteria may be amplified by the strain dynamics; in particular, the extent to which resistant strains outcompete susceptible strains under antimicrobial pressure may depend not only on the antimicrobial treatment strategies but also on the epidemiological parameters, such as the composition of the bacterial strains in a pig. This study evaluated how variation in the dosing protocol for intramuscular administration of tetracycline and the composition of bacterial strains in a pig affect the level of resistance in the intestine of a pig. Predictions were generated by a mathematical model of competitive growth of Escherichia coli strains in pigs under specified plasma concentration profiles of tetracycline. All dosing regimens result in a clear growth advantage for resistant strains. Short treatment duration was found to be preferable, since it allowed less time for resistant strains to outcompete the susceptible ones. Dosing frequency appeared to be ineffective at reducing the resistance levels. The number of competing strains had no apparent effect on the resistance level during treatment, but possession of fewer strains reduced the time to reach equilibrium after the end of treatment. To sum up, epidemiological parameters may have more profound influence on growth dynamics than dosing regimens and should be considered when designing improved treatment protocols.

How fitness reduced, antimicrobial resistant bacteria survive and spread: a multiple pig-multiple bacterial strain model

More than 30% of E. coli strains sampled from pig farms in Denmark over the last five years were resistant to the commonly used antimicrobial tetracycline. This raises a number of questions: How is this high level sustained if resistant bacteria have reduced growth rates? Given that there are multiple susceptible and resistant bacterial strains in the pig intestines, how can we describe their coexistence? To what extent does the composition of these multiple strains in individual pigs influence the total bacterial population of the pig pen? What happens to a complex population when antimicrobials are used? To investigate these questions, we created a model where multiple strains of bacteria coexist in the intestines of pigs sharing a pen, and explored the parameter limits of a stable system; both with and without an antimicrobial treatment. The approach taken is a deterministic bacterial population model with stochastic elements of bacterial distributions and transmission. The rates that govern the model are process-oriented to represent growth, excretion, and uptake from environment, independent of herd and meta-population structures. Furthermore, an entry barrier and elimination process for the individual strains in each pig were implemented. We demonstrate how competitive growth between multiple bacterial strains in individual pigs, and the transmission between pigs in a pen allow for strains of antimicrobial resistant bacteria to persist in a pig population to different extents, and how quickly they can become dominant if antimicrobial treatment is initiated. The level of spread depends in a non-linear way of the parameters that govern excretion and uptake. Furthermore, the sampling of initial distributions of strains and stochastic transmission events give rise to large variation in how homogenous and how resistant the bacterial population becomes. Most important: resistant bacteria are demonstrated to survive with a disadvantage in growth rate of well over 10%.

An individual-based model of transmission of resistant bacteria in a veterinary teaching hospital

Veterinary nosocomial infections caused by antibiotic resistant bacteria cause increased morbidity, higher cost and length of treatment and increased zoonotic risk because of the difficulty in treating them. In this study, an individual-based model was developed to investigate the effects of movements of canine patients among ten areas (transmission points) within a veterinary teaching hospital, and the effects of these movements on transmission of antibiotic susceptible and resistant pathogens. The model simulates contamination of transmission points, healthcare workers, and patients as well as the effects of decontamination of transmission points, disinfection of healthcare workers, and antibiotic treatments of canine patients. The model was parameterized using data obtained from hospital records, information obtained by interviews with hospital staff, and the published literature. The model suggested that transmission resulting from contact with healthcare workers was common, and that certain transmission points (housing wards, diagnostics room, and the intensive care unit) presented higher risk for transmission than others (lobby and surgery). Sensitivity analyses using a range of parameter values demonstrated that the risk of acquisition of colonization by resistant pathogens decreased with shorter patient hospital stays (P<0.0001), more frequent decontamination of transmission points and disinfection of healthcare workers (P<0.0001) and better compliance of healthcare workers with hygiene practices (P<0.0001). More frequent decontamination of heavily trafficked transmission points was especially effective at reducing transmission of the model pathogen.

A population model evaluating the consequences of the evolution of double-resistance and tradeoffs on the benefits of two-drug antibiotic treatments

The evolution of antibiotic resistance in microbes poses one of the greatest challenges to the management of human health. Because addressing the problem experimentally has been difficult, research on strategies to slow the evolution of resistance through the rational use of antibiotics has resorted to mathematical and computational models. However, despite many advances, several questions remain unsettled. Here we present a population model for rational antibiotic usage by adding three key features that have been overlooked: 1) the maximization of the frequency of uninfected patients in the human population rather than the minimization of antibiotic resistance in the bacterial population, 2) the use of cocktails containing antibiotic pairs, and 3) the imposition of tradeoff constraints on bacterial resistance to multiple drugs. Because of tradeoffs, bacterial resistance does not evolve directionally and the system reaches an equilibrium state. When considering the equilibrium frequency of uninfected patients, both cycling and mixing improve upon single-drug treatment strategies. Mixing outperforms optimal cycling regimens. Cocktails further improve upon aforementioned strategies. Moreover, conditions that increase the population frequency of uninfected patients also increase the recovery rate of infected individual patients. Thus, a rational strategy does not necessarily result in a tragedy of the commons because benefits to the individual patient and general public are not in conflict. Our identification of cocktails as the best strategy when tradeoffs between multiple-resistance are operating could also be extended to other host-pathogen systems. Cocktails or other multiple-drug treatments are additionally attractive because they allow re-using antibiotics whose utility has been negated by the evolution of single resistance.

Mathematical modeling on bacterial resistance to multiple antibiotics caused by spontaneous mutations

We formulate a mathematical model that describes the population dynamics of bacteria exposed to multiple antibiotics simultaneously, assuming that acquisition of resistance is through mutations due to antibiotic exposure. Qualitative analysis reveals the existence of a free-bacteria equilibrium, resistant-bacteria equilibrium and an endemic equilibrium where both bacteria coexist.

A modeling framework for the evolution and spread of antibiotic resistance: literature review and model categorization

Antibiotic-resistant infections complicate treatment and increase morbidity and mortality. Mathematical modeling has played an integral role in improving our understanding of antibiotic resistance. In these models, parameter sensitivity is often assessed, while model structure sensitivity is not. To examine the implications of this, we first reviewed the literature on antibiotic-resistance modeling published between 1993 and 2011. We then classified each article's model structure into one or more of 6 categories based on the assumptions made in those articles regarding within-host and population-level competition between antibiotic-sensitive and antibiotic-resistant strains. Each model category has different dynamic implications with respect to how antibiotic use affects resistance prevalence, and therefore each may produce different conclusions about optimal treatment protocols that minimize resistance. Thus, even if all parameter values are correctly estimated, inferences may be incorrect because of the incorrect selection of model structure. Our framework provides insight into model selection.

Antibiotic reduction campaigns do not necessarily decrease bacterial resistance: the example of methicillin-resistant Staphylococcus aureus

Interventions designed to reduce antibiotic consumption are under way worldwide. While overall reductions are often achieved, their impact on the selection of antibiotic-resistant selection cannot be assessed accurately from currently available data. We developed a mathematical model of methicillin-sensitive and methicillin-resistant Staphylococcus aureus (MSSA and MRSA) transmission inside and outside the hospital. A systematic simulation study was then conducted with two objectives: to assess the impact of antibiotic class-specific changes during an antibiotic reduction period and to investigate the interactions between antibiotic prescription changes in the hospital and the community. The model reproduced the overall reduction in MRSA frequency in French intensive-care units (ICUs) with antibiotic consumption in France from 2002 to 2003 as an input. However, the change in MRSA frequency depended on which antibiotic classes changed the most, with the same overall 10% reduction in antibiotic use over 1 year leading to anywhere between a 69% decrease and a 52% increase in MRSA frequency in ICUs and anywhere between a 37% decrease and a 46% increase in the community. Furthermore, some combinations of antibiotic prescription changes in the hospital and the community could act in a synergistic or antagonistic way with regard to overall MRSA selection. This study shows that class-specific changes in antibiotic use, rather than overall reductions, need to be considered in order to properly anticipate the impact of an antibiotic reduction campaign. It also highlights the fact that optimal gains will be obtained by coordinating interventions in hospitals and in the community, since the effect of an intervention in a given setting may be strongly affected by exogenous factors.

Modelling the transmission of healthcare associated infections: a systematic review

Background

Dynamic transmission models are increasingly being used to improve our understanding of the epidemiology of healthcare-associated infections (HCAI). However, there has been no recent comprehensive review of this emerging field. This paper summarises how mathematical models have informed the field of HCAI and how methods have developed over time.

Methods

MEDLINE, EMBASE, Scopus, CINAHL plus and Global Health databases were systematically searched for dynamic mathematical models of HCAI transmission and/or the dynamics of antimicrobial resistance in healthcare settings.

Results

In total, 96 papers met the eligibility criteria. The main research themes considered were evaluation of infection control effectiveness (64%), variability in transmission routes (7%), the impact of movement patterns between healthcare institutes (5%), the development of antimicrobial resistance (3%), and strain competitiveness or co-colonisation with different strains (3%). Methicillin-resistant Staphylococcus aureus was the most commonly modelled HCAI (34%), followed by vancomycin resistant enterococci (16%). Other common HCAIs, e.g. Clostridum difficile, were rarely investigated (3%). Very few models have been published on HCAI from low or middle-income countries.

The first HCAI model has looked at antimicrobial resistance in hospital settings using compartmental deterministic approaches. Stochastic models (which include the role of chance in the transmission process) are becoming increasingly common. Model calibration (inference of unknown parameters by fitting models to data) and sensitivity analysis are comparatively uncommon, occurring in 35% and 36% of studies respectively, but their application is increasing. Only 5% of models compared their predictions to external data.

Conclusions

Transmission models have been used to understand complex systems and to predict the impact of control policies. Methods have generally improved, with an increased use of stochastic models, and more advanced methods for formal model fitting and sensitivity analyses. Insights gained from these models could be broadened to a wider range of pathogens and settings. Improvements in the availability of data and statistical methods could enhance the predictive ability of models.